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Phase-Fitted and Amplification-Fitted Higher Order Two-Derivative Runge-Kutta Method for the Numerical Solution of Orbital and Related Periodical IVPs

N. A. Ahmad, N. Senu, F. Ismail
2017 Mathematical Problems in Engineering  
A phase-fitted and amplification-fitted two-derivative Runge-Kutta (PFAFTDRK) method of high algebraic order for the numerical solution of first-order Initial Value Problems (IVPs) which possesses oscillatory solutions is derived. We present a sixth-order four-stage two-derivative Runge-Kutta (TDRK) method designed using the phase-fitted and amplification-fitted property. The stability of the new method is analyzed. The numerical experiments are carried out to show the efficiency of the derived
more » ... ency of the derived methods in comparison with other existing Runge-Kutta (RK) methods.
doi:10.1155/2017/1871278 fatcat:2dvqwkfa5fbonal6igcwbtkdty